# A triangle has corners A, B, and C located at (7 ,3 ), (4 ,8 ), and (3 , 4 ), respectively. What are the endpoints and length of the altitude going through corner C?

Feb 3, 2016

#### Explanation:

this an isosceles triangle, you can show it by calculating the
$A C = B C$
distance formula $\sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}$
Thus:
$\sqrt{{4}^{2} + {1}^{2}} = 4.123$
$\sqrt{{1}^{2} + {4}^{2}} = 4.123$
So the midpoint of the base should be the altitude since it will also be the perpendicular bisector.
Now subtracting point A from B
You will find the horizontal a d vertical separation to be (3,-5)
half these separation, (1.5, -2.5), add to B(4,8) or subtract fromA(7, 3)
And get the point (5.5,5.5) this is the altitude of our isosceles triangle...